Critical Temperature for Peng Robinson Equation using Alpha-function and Pure Component Parameter Calculator

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Peng Robinson Model of Real Gas

Berthelot and Modified Berthelot Model of Real Gas

Clausius Model of Real Gas

Redlich Kwong Model of Real Gas

Saturation Vapour Pressure

Specific Heat Capacity

Van der Waals Force

Wohl Model of Real Gas

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Critical Temperature

Critical Pressure

Peng Robinson Parameter

Reduced Pressure

Reduced Temperature

✖Temperature is the degree or intensity of heat present in a substance or object.ⓘ Temperature [T]			+10% -10%
✖α-function is a function of temperature and the acentric factor.ⓘ α-function [α]			+10% -10%
✖Pure Component Parameter is a function of the acentric factor.ⓘ Pure Component Parameter [k]			+10% -10%

✖Critical Temperature is the highest temperature at which the substance can exist as a liquid. At this phase boundaries vanish, and the substance can exist both as a liquid and vapor.ⓘ Critical Temperature for Peng Robinson Equation using Alpha-function and Pure Component Parameter [T_c]

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Formula

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Critical Temperature for Peng Robinson Equation using Alpha-function and Pure Component Parameter

Formula

`"T"_{"c"} = "T"/((1-((sqrt("α")-1)/"k"))^2)`

Example

`"101.0488K"="85K"/((1-((sqrt("2")-1)/"5"))^2)`

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Critical Temperature for Peng Robinson Equation using Alpha-function and Pure Component Parameter Solution

STEP 0: Pre-Calculation Summary

Formula Used

Critical Temperature = Temperature/((1-((sqrt(α-function)-1)/Pure Component Parameter))^2)
T_c = T/((1-((sqrt(α)-1)/k))^2)
This formula uses 1 Functions, 4 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Critical Temperature - (Measured in Kelvin) - Critical Temperature is the highest temperature at which the substance can exist as a liquid. At this phase boundaries vanish, and the substance can exist both as a liquid and vapor.
Temperature - (Measured in Kelvin) - Temperature is the degree or intensity of heat present in a substance or object.
α-function - α-function is a function of temperature and the acentric factor.
Pure Component Parameter - Pure Component Parameter is a function of the acentric factor.

STEP 1: Convert Input(s) to Base Unit

Temperature: 85 Kelvin --> 85 Kelvin No Conversion Required
α-function: 2 --> No Conversion Required
Pure Component Parameter: 5 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_c = T/((1-((sqrt(α)-1)/k))^2) --> 85/((1-((sqrt(2)-1)/5))^2)

Evaluating ... ...

T_c = 101.048828581759

STEP 3: Convert Result to Output's Unit

101.048828581759 Kelvin --> No Conversion Required

FINAL ANSWER

101.048828581759 ≈ 101.0488 Kelvin <-- Critical Temperature

(Calculation completed in 00.004 seconds)

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< 8 Critical Temperature Calculators

Critical Temperature using Peng Robinson Equation given Reduced and Critical Parameters

Go Critical Temperature = (((Reduced Pressure*Critical Pressure)+(((Peng–Robinson Parameter a*α-function)/(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson Parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson Parameter b^2)))))*(((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson Parameter b)/[R]))/Reduced Temperature

Critical Temperature using Peng Robinson Equation given Reduced and Actual Parameters

Go Real Gas Temperature = ((Pressure+(((Peng–Robinson Parameter a*α-function)/((Molar Volume^2)+(2*Peng–Robinson Parameter b*Molar Volume)-(Peng–Robinson Parameter b^2)))))*((Molar Volume-Peng–Robinson Parameter b)/[R]))/Reduced Temperature

Critical Temperature given Peng Robinson Parameter a, and other Actual and Reduced Parameters

Go Critical Temperature = sqrt((Peng–Robinson Parameter a*(Pressure/Reduced Pressure))/(0.45724*([R]^2)))

Critical Temperature given Peng Robinson Parameter b and other Actual and Reduced Parameters

Go Critical Temperature = (Peng–Robinson Parameter b*(Pressure/Reduced Pressure))/(0.07780*[R])

Critical Temperature for Peng Robinson Equation using Alpha-function and Pure Component Parameter

Go Critical Temperature = Temperature/((1-((sqrt(α-function)-1)/Pure Component Parameter))^2)

Critical Temperature of Real Gas using Peng Robinson Equation given Peng Robinson Parameter a

Go Critical Temperature = sqrt((Peng–Robinson Parameter a*Critical Pressure)/(0.45724*([R]^2)))

Critical Temperature of Real Gas using Peng Robinson Equation given Peng Robinson Parameter b

Go Critical Temperature = (Peng–Robinson Parameter b*Critical Pressure)/(0.07780*[R])

Critical Temperature given Inversion Temperature

Go Critical Temperature = (4/27)*Inversion Temperature

Critical Temperature for Peng Robinson Equation using Alpha-function and Pure Component Parameter Formula

Critical Temperature = Temperature/((1-((sqrt(α-function)-1)/Pure Component Parameter))^2)
T_c = T/((1-((sqrt(α)-1)/k))^2)

What are Real Gases?

Real gases are non ideal gases whose molecules occupy space and have interactions; consequently, they do not adhere to the ideal gas law. To understand the behavior of real gases, the following must be taken into account:
- compressibility effects;
- variable specific heat capacity;
- van der Waals forces;
- non-equilibrium thermodynamic effects;
- issues with molecular dissociation and elementary reactions with variable composition.

How to Calculate Critical Temperature for Peng Robinson Equation using Alpha-function and Pure Component Parameter?

Critical Temperature for Peng Robinson Equation using Alpha-function and Pure Component Parameter calculator uses Critical Temperature = Temperature/((1-((sqrt(α-function)-1)/Pure Component Parameter))^2) to calculate the Critical Temperature, The Critical Temperature for Peng Robinson Equation using Alpha-function and Pure Component Parameter formula is defined as the highest temperature at which the substance can exist as a liquid. Critical Temperature is denoted by T_c symbol.

How to calculate Critical Temperature for Peng Robinson Equation using Alpha-function and Pure Component Parameter using this online calculator? To use this online calculator for Critical Temperature for Peng Robinson Equation using Alpha-function and Pure Component Parameter, enter Temperature (T), α-function (α) & Pure Component Parameter (k) and hit the calculate button. Here is how the Critical Temperature for Peng Robinson Equation using Alpha-function and Pure Component Parameter calculation can be explained with given input values -> 101.0488 = 85/((1-((sqrt(2)-1)/5))^2).

FAQ

What is Critical Temperature for Peng Robinson Equation using Alpha-function and Pure Component Parameter?

The Critical Temperature for Peng Robinson Equation using Alpha-function and Pure Component Parameter formula is defined as the highest temperature at which the substance can exist as a liquid and is represented as T_c = T/((1-((sqrt(α)-1)/k))^2) or Critical Temperature = Temperature/((1-((sqrt(α-function)-1)/Pure Component Parameter))^2). Temperature is the degree or intensity of heat present in a substance or object, α-function is a function of temperature and the acentric factor & Pure Component Parameter is a function of the acentric factor.

How to calculate Critical Temperature for Peng Robinson Equation using Alpha-function and Pure Component Parameter?

The Critical Temperature for Peng Robinson Equation using Alpha-function and Pure Component Parameter formula is defined as the highest temperature at which the substance can exist as a liquid is calculated using Critical Temperature = Temperature/((1-((sqrt(α-function)-1)/Pure Component Parameter))^2). To calculate Critical Temperature for Peng Robinson Equation using Alpha-function and Pure Component Parameter, you need Temperature (T), α-function (α) & Pure Component Parameter (k). With our tool, you need to enter the respective value for Temperature, α-function & Pure Component Parameter and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Critical Temperature?

In this formula, Critical Temperature uses Temperature, α-function & Pure Component Parameter. We can use 6 other way(s) to calculate the same, which is/are as follows -

Critical Temperature = sqrt((Peng–Robinson Parameter a*(Pressure/Reduced Pressure))/(0.45724*([R]^2)))
Critical Temperature = (Peng–Robinson Parameter b*(Pressure/Reduced Pressure))/(0.07780*[R])
Critical Temperature = sqrt((Peng–Robinson Parameter a*Critical Pressure)/(0.45724*([R]^2)))
Critical Temperature = (Peng–Robinson Parameter b*Critical Pressure)/(0.07780*[R])
Critical Temperature = (((Reduced Pressure*Critical Pressure)+(((Peng–Robinson Parameter a*α-function)/(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson Parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson Parameter b^2)))))*(((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson Parameter b)/[R]))/Reduced Temperature
Critical Temperature = (4/27)*Inversion Temperature

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